**Suresh Alapati**

**Method**

School of Mechanical & Mechatronics Engineering, Kyungsung University, 309, Suyeong-ro (Daeyeon-dong), Nam-gu, Busan 48434, Korea; sureshalapatimech@gmail.com or suresh@ks.ac.kr; Tel.: +82-51-663-4690

 **a** 

**Smoothed**

**Concentric**

**Boltzmann**

**Profile**

Received: 3 June 2020; Accepted: 23 June 2020; Published: 26 June 2020

**Abstract:** This research work presents results obtained from the simulation of natural convection inside a concentric hexagonal annulus by using the lattice Boltzmann method (LBM). The fluid flow (pressure and velocity fields) inside the annulus is evaluated by LBM and a finite difference method (FDM) is used to ge<sup>t</sup> the temperature filed. The isothermal and no-slip boundary conditions (BC) on the hexagonal edges are treated with a smooth profile method (SPM). At first, for validating the present simulation technique, a standard benchmarking problem of natural convection inside a cold square cavity with a hot circular cylinder is simulated. Later, natural convection simulations inside the hexagonal annulus are carried out for different values of the aspect ratio, *AR* (ratio of the inner and outer hexagon sizes), and the Rayleigh number, Ra. The simulation results are presented in terms of isotherms (temperature contours), streamlines, temperature, and velocity distributions inside the annulus. The results show that the fluid flow intensity and the size and number of vortex pairs formed inside the annulus strongly depend on *AR* and Ra values. Based on the concentric isotherms and weak fluid flow intensity at the low Ra, it is observed that the heat transfer inside the annulus is dominated by the conduction mode. However, multiple circulation zones and distorted isotherms are observed at the high Ra due to the strong convective flow. To further access the accuracy and robustness of the present scheme, the present simulation results are compared with the results given by the commercial software, ANSYS-Fluent®. For all combinations of *AR* and Ra values, the simulation results of streamlines and isotherms patterns, and temperature and velocity distributions inside the annulus are in very good agreemen<sup>t</sup> with those of the Fluent software.

**Keywords:** lattice Boltzmann method; smoothed profile method; hybrid method; natural convection simulation; concentric hexagonal annulus
